eBook ISBN:  9780821881231 
Product Code:  CONM/444.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
eBook ISBN:  9780821881231 
Product Code:  CONM/444.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsContemporary MathematicsVolume: 444; 2007; 228 ppMSC: Primary 37; 42; 47; 60; 65
There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. The breakthrough achieved by Tao and Green is attributed to applications of techniques from ergodic theory and harmonic analysis to problems in number theory.
Articles in the present volume are based on talks delivered by plenary speakers at a conference on Harmonic Analysis and Ergodic Theory (DePaul University, Chicago, December 2–4, 2005). Of ten articles, four are devoted to ergodic theory and six to harmonic analysis, although some may fall in either category. The articles are grouped in two parts arranged by topics. Among the topics are ergodic averages, central limit theorems for random walks, Borel foliations, ergodic theory and low pass filters, data fitting using smooth surfaces, Nehari's theorem for a polydisk, uniqueness theorems for multidimensional trigonometric series, and Bellman and \(s\)functions.
In addition to articles on current research topics in harmonic analysis and ergodic theory, this book contains survey articles on convergence problems in ergodic theory and uniqueness problems on multidimensional trigonometric series.
ReadershipResearch mathematicians interested in harmonic analysis, ergodic theory, and their interaction.

Table of Contents

Articles

Ahmed I. Zayed — Topics in ergodic theory and harmonic analysis: an overview [ MR 2423620 ]

Joseph Rosenblatt — The mathematical work of Roger Jones [ MR 2423621 ]

Yves Derriennic and Michael Lin — The central limit theorem for random walks on orbits of probability preserving transformations [ MR 2423622 ]

Richard F. Gundy — Probability, ergodic theory, and lowpass filters [ MR 2423623 ]

Daniel J. Rudolph — Ergodic theory on Borel foliations by $\Bbb R^n$ and $\Bbb Z^n$ [ MR 2423624 ]

Grant V. Welland — Short review of the work of Professor J. Marshall Ash [ MR 2423625 ]

J. Marshall Ash and Gang Wang — Uniqueness questions for multiple trigonometric series [ MR 2423626 ]

Charles Fefferman — Smooth interpolation of functions on $\Bbb R^n$ [ MR 2423627 ]

Paul Alton Hagelstein — Problems in interpolation theory related to the almost everywhere convergence of Fourier series [ MR 2423628 ]

Michael T. Lacey — Lectures on Nehari’s theorem on the polydisk [ MR 2423629 ]

Leonid Slavin and Alexander Volberg — The $s$function and the exponential integral [ MR 2423630 ]


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There are strong connections between harmonic analysis and ergodic theory. A recent example of this interaction is the proof of the spectacular result by Terence Tao and Ben Green that the set of prime numbers contains arbitrarily long arithmetic progressions. The breakthrough achieved by Tao and Green is attributed to applications of techniques from ergodic theory and harmonic analysis to problems in number theory.
Articles in the present volume are based on talks delivered by plenary speakers at a conference on Harmonic Analysis and Ergodic Theory (DePaul University, Chicago, December 2–4, 2005). Of ten articles, four are devoted to ergodic theory and six to harmonic analysis, although some may fall in either category. The articles are grouped in two parts arranged by topics. Among the topics are ergodic averages, central limit theorems for random walks, Borel foliations, ergodic theory and low pass filters, data fitting using smooth surfaces, Nehari's theorem for a polydisk, uniqueness theorems for multidimensional trigonometric series, and Bellman and \(s\)functions.
In addition to articles on current research topics in harmonic analysis and ergodic theory, this book contains survey articles on convergence problems in ergodic theory and uniqueness problems on multidimensional trigonometric series.
Research mathematicians interested in harmonic analysis, ergodic theory, and their interaction.

Articles

Ahmed I. Zayed — Topics in ergodic theory and harmonic analysis: an overview [ MR 2423620 ]

Joseph Rosenblatt — The mathematical work of Roger Jones [ MR 2423621 ]

Yves Derriennic and Michael Lin — The central limit theorem for random walks on orbits of probability preserving transformations [ MR 2423622 ]

Richard F. Gundy — Probability, ergodic theory, and lowpass filters [ MR 2423623 ]

Daniel J. Rudolph — Ergodic theory on Borel foliations by $\Bbb R^n$ and $\Bbb Z^n$ [ MR 2423624 ]

Grant V. Welland — Short review of the work of Professor J. Marshall Ash [ MR 2423625 ]

J. Marshall Ash and Gang Wang — Uniqueness questions for multiple trigonometric series [ MR 2423626 ]

Charles Fefferman — Smooth interpolation of functions on $\Bbb R^n$ [ MR 2423627 ]

Paul Alton Hagelstein — Problems in interpolation theory related to the almost everywhere convergence of Fourier series [ MR 2423628 ]

Michael T. Lacey — Lectures on Nehari’s theorem on the polydisk [ MR 2423629 ]

Leonid Slavin and Alexander Volberg — The $s$function and the exponential integral [ MR 2423630 ]